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Statistics arose in part out of the interplay between mathematics and the data-analytic needs of various applied sciences (Stigler 1999). Close linkages to mathematics and to research-oriented fields have prompted debate over the emergence of statistics as a distinct field of study. Efforts to differentiate statistics from mathematics have drawn attention to its unique history, questions, and content. Insofar as statistics is an evolving subject area, with academic and practical ties to a number of disciplines and professions, it continues to benefit from the examination of its origins, nature, and unfolding. This article contributes to this general goal through a review of (a) early definitions of statistics, (b) recent discussions of disciplinary boundaries, (c) twentieth-century reform views on including statistics topics in school mathematics, and (d) the impact of curricular and pedagogic factors on the uniformity of the discipline.

Over the course of the twentieth century, statistics developed into a distinct field of study (Stigler 1986). However, the emergence of statistics as a "separate discipline" (Moore 1988, p. 3) has been shaped by diverse intellectual origins, interstitial applications, and curricular and pedagogic reforms. Moore (1998) argued that statistics is not a branch of mathematics but rather "an independent discipline" (p. 1254), with its own unique origins, questions, and content. Of late, academic statisticians have made efforts to clarify linkages with the domain of mathematics and the data-analytic needs of various applied sciences. This article extends Moore's and others' work by reviewing (a) the historical roots of statistics, (b) the recent debate over disciplinary boundaries, (c) the twentieth-century reform movement to include statistics topics in school mathematics, and (d) the impact of curricular and pedagogic factors on the uniformity of the discipline. The purpose here is not solely to articulate differ ences between statistics and mathematics but also to discuss historical and developmental challenges to the widespread recognition of statistics as an independent field. This perspective reveals that some of the most distinctive aspects of statistics, for example, "data analysis" and "scientific inference" (Moore 2000, p. 9), emanate from its coalescent foundations and myriad applications.

2. EARLY USES OF THE TERM "STATISTICS": DATA AND INFERENCE

Both the term and the discipline of statistics share a lengthy and enigmatic past. Although authors interested in the history of statistics do not always agree on its precise origins, many mention the ancient surveys conducted for fiscal and military purposes. Hald (1990) noted the quinquennial censuses of people and property in the Roman Republic, indirectly suggesting. that the collection of such data was a precursor to descriptive statistics. He traced the word "statistics" to sixteenth-century Italian roots, meaning the assemblage of information and facts of interest to a statesman (statista) or pertaining to the stato (stato). Pearson (1978) also discussed an early (i.e., seventeenth-century) branch of knowledge called "Statistik" that dealt with matters of the state and constitutional history. However, Pearson (1978) differentiated this principally non-numerical "hybrid discipline of statecraft" (p. 2) from modern inferential statistics. Kendall (1960) amplified this distinction in stating that, "to beg in a history of statistics with references to endeavours in the ancient world to record information about states....is to fail to understand either the basis of the statistical approach or the nature of the statistical method" (p. 447).

Graunt's (1662) descriptive (statistical) analysis of mortality rates and causes of death in seventeenth-century London is considered one of the earliest examples of what was then referred to as "Political Arithmetic" and what is now termed statistics (see Hald 1990). …

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